Telehealth private practice in NJ, but seeing clients in NY and NJ

Yes, you will need to file a NY return to claim the income from the patients you see remotely in NY.  NY is one of the few states that tax remote workers unless they have a need to work remotely for THEIR EMPLOYERS convenience.  Since you are self-employed, and your clients that you are seeing are inside of NY, even though you are outside of NY, this would be considered NY sourced income. 

You will only be taxed on the income that is from the patients who are in NY.  When you file, you will want to fill out your NY Non-Resident return first, then you will file your NJ state return claiming a credit for taxes paid to NY.  This keeps you from being double taxed on the same income.   If the non resident state had a higher tax rate than your resident state, your credit will be limited to the amount of tax you would have paid to your resident state.  They will not give you a refund of the taxes you paid to the nonresident state. 

Multiple States

File Non Resident State Return